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Question

Let ln=2n+(2)n2n and Ln=2n+(2)n3n then as n

A
Both the sequences have limits.
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B
limnln exists but limnLn does not exist.
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C
limnln does not exist but limnLn exists.
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D
Both the sequences do not have limits.
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Solution

The correct option is C limnln does not exist but limnLn exists.
ln=2n+(2)n2n=1+(1)nlimnln={0 if n is odd2 if n is even

So, limnln does not exist.

Ln=(23)n(1+(1)n)
limnLn=0

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